Volume 1 PROGRESS IN PHYSICS January, 2010
Is Fundamental Particle Mass 4
π
Quantized?
Robert A. Stone Jr.
1313 Connecticut Ave, Bridgeport, CT 06484, USA E-mail: [email protected]
The Standard Model lacks an explanation for the specific mass values of the fundamen-tal particles. This is to report that a single spin quantized mass formula can produce the masses of the proton, theW, and the three electron generations. The 4πmass quanti-zation pattern limits the electron generations to three, while the particle’s generational property is one of the components of the proposed intra-particle quantization process. Although the developed relationships are presently phenomenological, so was Bohr’s atomic quantization proposal that lead to quantum mechanics.
1 Introduction
In an attempt to understand the reason for particle mass values, several authors have looked for mass relationships among the known particles.
Nambu [1] suggested that quark composite particle mass may be quantized, showing a 70 MeV quantization pattern.
Palazzi [2] (2007) revisits this hypothesis for mesons showing that this quantization pattern is statistically real.
Ne’eman and Sijacki [3] use the SL(4,R) group and spin (1/2,3/2,5/2, etc.) to produce the Regge trajectory like behav-ior of quark particle masses suggesting the possibility that mass may be spin quantized.
What has not been seen is that given the experimen-tal and theoretical uncertainty, the measured W± mass of 80398±25 MeV [4] is exactly 2mp/me(3672.30534) times
the mass value symmetrically between the electron and the proton (√mpme =21.89648319 MeV), i.e. 80410.57 MeV.
2 Fundamental particle mass, a spin quantized process?
Taking a mass symmetric approach to fundamental particle mass leads to an eloquently simple spin quantized mass rela-tionship between the stable spin 1/2 electron and proton mass and the unstable spin 1W±particle mass given by
mx=Msp
2S mp/me
(S C M)
, (1)
where x is {p,e,W}, the mass symmetry point Msp is 21.89648319 MeV, S is the spin quantum number{1
2,1},C
is the charge quantum number{±1}, andMis the matter type quantum number{matter= +, anti-matter=−}.
Thus equation (1) is both mass and charge up/down sym-metric, spin quantized and indicates Nature may be funda-mentally mass symmetric.
As indicated in §9, this mass up/down symmetry is in keeping with the measured cosmological constant.
3 Nature’s constants, as functions of 4π
Proposing natures coupling constants are a function of 4πand the fine structure coupling constant and the weak (angle)
cou-pling constant are connected to mass, yields the following 4π definitions.
The fine structure constantαcs = πς(4π̺)−2/(2
√
2), the charged weak angle αsg = 2
√
2(4π̺)−1
(∼.2344 vs .2312 [5]), where “g” is the other force that couples to produce the weak coupling constant. The relationship to mass is πme/mp = αcsαsg = αcg = πς(4π̺)−3 and thus mp/me =
(4π̺)3/ς. The uncharged (neutrino) weak angle αsg(1) =
2√2(4π1)−1
(∼.2251 vs .2277 [6]). The new constant̺ =
αcsαsg(1)mp/(meπ)= 0.959973785 andς=(4π̺)3me/mp=
0.956090324.
4 Fundamental particle mass, a 4πquantized process?
Equation (1) rewritten with the 4πdefinition of mp/me re-sults in
mx=Msp
2S(4π̺)3/ς(S C M). (2)
In addition to being spin quantized, equation (2) indicates that the fundamental particle mass quantization process is a func-tion of (4π)x. For example, the pure theorymp(1,1)/me(1,1)ratio
(̺ =1, ς =1) is exactly (4π)3 where the deviation from the pure theory 4πquantization process is given by̺.
5 Three electron generations, a 4πquantized process?
The electron generational mass ratios also appear to be a func-tion of (4π̺x)xor more precisely (4π̺x)(3−x)
.
The first (x = 1) mass ratio µ to e (i.e me1/me0) is
√
2(4π̺1)(3−1)where̺1 =.962220482 while the second (x=
2) mass ratiome2/me1is
√
2(4π̺2)(3−2)with̺2=.946279794.
Note that̺and̺xare believed to be the deviation from pure theory for two separate frequency components of the quantization processes.
Thus the form of the first and second (x=1,2) genera-tion mass ratios (me(x)/me(x−1)) is
√
2(4π̺x)3−x. The deviation from the generational pure theory 4πquantization process in-creases (smaller̺x) with higher generations.
This√2(4π)3−xpattern also results in thex=3 mass ratio (me3/me2) of (4π)(3−3)
, i.e. no higher (4π)x quantized mass states and thus no higher generations.
January, 2010 PROGRESS IN PHYSICS Volume 1
The similarity of 4πquantization allows the fundamental particle equation (1) to be combined with the generational re-lationship into a single phenomenological equation given by,
mx=Msp(n)
2S(4π̺)3/ς(S C M), (3)
where Msp(n) =Msp S−n/2(4π̺n)(6S n−S n(n+1)) and̺n = 1 − log(1+64.75639n/S)/(112S) are used and generation n is
{0,1,2}.
From (3), the me1 (µ) mass is 105.6583668 MeV (µ =
105.6583668±.0000038 MeV [4]) and theme2 (τ) mass is 1776.83 MeV (τ= 1776.84±.17 MeV [4]).
Remember that even though both̺n, and̺represent devi-ations from the pure theory (4π)xquantization nature of these particles’ masses, their cause is understood to be related to two separate quantization process components.
6 The Standard Model and quantization
First, the quantization proposition is not in conflict with the existence of quarks. Rather quantization is an additional constraint. The quantization proposition is that if there is a (pseudo-) stable frequency quantized state, then there is an observed (persistent) massed particle resulting in;
1) a specific stable quantization state energy/mass or 2) a pseudo-stable quantized decay mass value.
Thus the quantization process constrains the stable parti-cle base mass or unstable partiparti-cle decay point mass while the types and symmetries of quarks construct the particle varia-tions seen in the “particle zoo”.
That quark composite particle masses are quantized was first suggested by Nambu [1] and recently statistically vali-dated by Palazzi [2]. The quantization increments cited are 70 (n=integer) and 35 MeV (n=odd or n=even) which are ap-proximately Msp πand Msp π/2. Thus for exampleη(547) has n=16 [2] and usingMspnπ/2 givesmη =Msp8π≃550.
A Regge trajectory like spin quantum number based quantization pattern is given by Ne’eman and Sijacki [3] where the particle’s measured mass vary about the predicted points. For the (3/2,1) group the points are approximately (20,22,24) π Msp, for the (5/2,2) group they are approxi-mately (24,26,28,30,32) π Msp, and for the (7/2,3) group they are approximately (28,30,32,34,36,38,40)πMsp.
Second, a quantizing mechanism as fundamental to the nature of massed particles is a natural explanation given QM’s quantized nature.
Third, an intra-particle quantization process minimally needs two intra-particle frequency components. Equation (3) suggests one component is related to the particle’s “invari-ant” mass/energy and a second component is related to the generational mass symmetry point. A generational compo-nent could be the source for and thus explain the genera-tional exchange seen in the muon neutrino nucleon interac-tionνµ+N→P++µ−. The generational component’s effect on the charged particle mass symmetry point isMsp(n).
Is the massed particle a “quantized photon”?
Is the first photonic component of the quantization pro-cess the underlying reason for the universality of Maxwell’s equations for both photons and charged particles?
Is the second quantizing component responsible for the intra-particle mass and charge quantization, for the genera-tional property, as well as the (inter-particle?) quantization of QM?
7 Equation 1 and new particles
If quantization is the source of (1) then, quark structure per-mitting, there may be a second generation proton. From the phenomenological equation (3),mp2≃194 GeV. This second generation proton is within LHC’s capabilities.
Note that equation (3) is phenomenological and another option exists for merging the electron generations.
Equation (1) also indicates the possibility of a new “lep-ton like” (mass down charge down) spin 1 lightW± parti-cle with a mass of ∼ 5.96 KeV (mlW). If such low fre-quency/energy quantization is possible, thelW±’s decay, like the W±’s decay, would be instantaneous. At KeV energy, attempted quantization may only result in enhanced photon production. At MeV energies,lW±pair production with in-stantaneous decay would look like an electron positron pair production but would actually belW− →e−+νandlW+
→
e++νdecays.
Finally, the super-symmetric (charge and mass symmet-ric) view that results from equation (1) can make some fun-damental Standard Model problems go away.
8 The matter only universe problem
The present SM has only a matter anti-matter mass creation process, yet we appear to have a matter only universe. This aspect is presently unaccounted for.
The super-symmetric view indicated by the charge and mass up/down symmetry of (1) and (2) enables the possibility of an alternate mechanism for fundamental particle creation.
This alternate process symmetrically breaks the electron and proton of the same mass (for eq. (2), at̺=(4π)−1, ς=1,
me=mp) into a proton of higher mass (up) and an electron of
lower mass (down), yielding a matter only universe.
9 The cosmological constant problem
Given the symmetric mass up/down symmetry breaking of (2) that produces a matter only universe, the symmetry break-ing contribution to the cosmological constant can be zero and thus consistent with the observed cosmological constant value. Based on the Standard Model’s view, QCD’s contribu-tion to the cosmological constant produces a value that is off
by 1046, i.e 46 orders of magnitude wrong [7], with no
sub-stantive resolution. Using the Standard Model view for the electroweak contribution results in an even greater error.
Volume 1 PROGRESS IN PHYSICS January, 2010
The preciseness of the predicted W± particle mass of equation (1) and the pattern of quantization shown via (2) and (3) call into question many of the Standard Model views and assumptions about the causality of the observed “invari-ant mass” values.
However, it is precisely the Standard Model view and the Standard Model symmetry breaking approach that results in these fundamental Standard Model problems. Maybe we should listen to these fundamental problems with more care.
10 Summary
The Standard Model is highly successful in many areas, espe-cially QM and QED. One of the open questions for the Stan-dard Model is the cause of the specific invariant mass values of fundamental particles.
The accepted Standard Model view hides the fact that the measuredW±mass of 80398±25 MeV [4] is exactly 2mp/me
(3672.30534) times the mass value symmetrically between the electron and the proton (Msp =(mpme)1/2) and the Stan-dard Model gives no reason for the electron generations nor their masses.
A mass and charge symmetric, 4π quantized and spin quantized mass formula is given that produces the exactW± particle mass. The electron generation mass ratios can be produced using a 4π related magnitude, i.eme(x)/me(x−1) =
√
2(4π̺x)3−xfor x=(1,2).
The common 4πformulation allows the single mass for-mula (3) to produce the masses of the proton, the W, and the three electron generations.
Equations (1), (2) and (3) strongly suggest several new aspects.
First, in addition to the atomic orbital quantization of QM, there is an intra-particle quantization mechanism which gives the fundamental particles and generations their invariant mass values.
Second, the fundamental particle quantization process is spin{12,1}and 4πquantized.
Third, equation (1) indicates that nature is actually highly symmetric, being charge and mass up/down symmetric.
This symmetry allows for the possibility of an alternate matter creation process for the early universe which results in creating only matter.
In addition the mass and charge super-symmetric view of equation (1) should yield a near zero cosmological constant in keeping with the observed value.
A quantization proposition is not in conflict with the ex-istence of quarks.
A dual approach is required to explain the 4π and spin mass pattern of equation (1), the 4πelectron generation mass pattern, and Palazzi’s [2] results.
This dual approach involves a quantizing mechanism as the source of the stability and mass value of the spin 1/2 par-ticles, the mass values of the fundamentalW±particles, and
the decay point mass of quark composites, while the types and symmetries of quarks construct the variations seen in the “particle zoo”.
The quantized view of equation (3) indicates that one of the intra-particle quantization components can be the source for the generational identity and a foundation for the gen-erational exchange seen in the muon neutrino interaction νµ+N→P++µ−.
Is “A quantized form of energy.” the answer to the ques-tion “What is mass?”.
If relationship (1) and the quantization interpretation of (1), (2) and (3) are fundamental, then the recognition of an intra-particle quantization process is required to move the Standard Model to a massed particle model.
Submitted on August 16, 2009/Accepted on August 25, 2009
References
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4. Amsler C. et al. Phys. Lett., 2008, v. B667, 1; Updated Par-ticle Data Group, ParPar-ticle Listings 2009 http://pdg.lbl.gov/2009/
listings/rpp2009-list-electron.pdf, rpp2009-list-muon.pdf, rpp2009-list-tau.pdf, rpp2009-list-p.pdf, rpp2009-list-w-boson.pdf.
5. Particle Data Group, Physical Constants 2009:
http://pdg.lbl.gov/2009/constants/rpp2009-phys-constants.pdf 6. Zeller G.P. et al. (NuTeV collaboration) Precise determination of
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